灰色二层多目标线性规划问题及其解法

针对二层多目标线性规划问题,结合灰色系统的特性,提出了一般灰色二层多目标线性规划问题,并给出了模型的相关定义和定理.针对漂移型灰色二层多目标线性规划问题,提出一种具有全局收敛性质的求解算法.首先通过线性加权模理想点法把多目标转化为单目标;然后当可行域为非空紧集时,利用库恩塔克条件把双层转化为单层,再利用粒子群算法搜索单目标单层线性规划即可得到原问题的解;最后通过算例表明了该算法的有效性.     

协同车辆路径问题的模糊规划模型和算法*

属于不同公司的配送中心共享车队、仓储等资源为客户协同配送货物的协同车辆路径问题是一个热点问题。考虑车辆行驶时间和顾客服务时间的不确定性,建立以车辆配送总费用最小为目标的一类带时间窗协同车辆路径问题模糊规划模型,将其进行清晰化处理使之转换为一类确定性数学模型,采用魏明等人的自适应离散粒子群算法求解该问题。最后通过一个算例得出结论：同普通物流配送情形相比,该模型求解的总配送里程和费用均有效减少,验证了模型的正确性和合理性。     

基于多元最优信息规划的微粒群优化算法

在改进型微粒群优化算法的基础上，考虑到运算初期避免陷入局部寻优的需要，将多元最优信息分布状态知识引入对微粒群的总体运动规划，构造了适于求解高维多峰函数寻优问题的微粒群算法．仿真结果显示，该方法比改进型微粒群算法具有更好的总体寻优特性．     

An interactive approach based on a discrete differential evolution algorithm for a class of integer bilevel programming problems

This paper presents an interactive approach based on a discrete differential evolution algorithm to solve a class of integer bilevel programming problems, in which integer decision variables are controlled by an upper-level decision maker and real-value or continuous decision variables are controlled by a lower-level decision maker. Using the Karush--Kuhn–Tucker optimality conditions in the lower-level programming, the original discrete bilevel formulation can be converted into a discrete single-level nonlinear programming problem with the complementarity constraints, and then the smoothing technique is applied to deal with the complementarity constraints. Finally, a discrete single-level nonlinear programming problem is obtained, and solved by an interactive approach. In each iteration, for each given upper-level discrete variable, a system of nonlinear equations including the lower-level variables and Lagrange multipliers is solved first, and then a discrete nonlinear programming problem only with inequality constraints is handled by using a discrete differential evolution algorithm. Simulation results show the effectiveness of the proposed approach.     

On bilevel multi-follower decision making: General framework and solutions

Within the framework of any bilevel decision problem, a leader’s decision is influenced by the reaction of his or her follower. When multiple followers who may have had a share in decision variables, objectives and constraints are involved in a bilevel decision problem, the leader’s decision will be affected, not only by the reactions of these followers, but also by the relationships among these followers. This paper firstly identifies nine different kinds of relationships (S₁ to S₉) amongst followers by establishing a general framework for bilevel multi-follower decision problems. For each of the nine a corresponding bilevel multi-follower decision model is then developed. Also, this paper particularly proposes related theories focusing on an uncooperative decision problem (i.e., S₁ model), as this model is the most basic one for bilevel multi-follower decision problems over the nine kinds of relationships. Moreover, this paper extends the Kuhn-Tucker approach for driving an optimal solution from the uncooperative decision model. Finally, a real case study of a road network problem illustrates the application of the uncooperative bilevel decision model and the proposed extended Kuhn-Tucker approach.     

基于改进粒子群算法的网络广告配置优化

针对网络广告的特点,提出了一个基于混合定价策略的网络广告资源配置优化模型,将其建模为一个约束优化问题,最大化网站的总收益。通过罚函数法进行约束处理,提出一种改进的粒子群算法进行求解。仿真结果表明了该算法的有效性。     

基于SQP 局部搜索的混沌粒子群优化算法

提出一种基于序贯二次规划(SQP)法的混沌粒子群优化方法(CPSO-SQP).将混沌PSO作为全局搜索器,并用SQP加速局部搜索,使得粒子能够在快速局部寻优的基础上对整个空间进行搜索,既保证了算法的收敛性,又大大增加了获得全局最优的几率.仿真结果表明,算法精度高、成功率大、全局收敛速度快,明显优于现有算法.将所提出的算法用于高密度聚乙烯(HDPE)装置串级反应过程的乙烯单耗优化,根据工业反应机理以及现场操作经验分析可知,所提出的算法是可行的.     

带有补偿的模糊产销计划模型及其混合算法

基于两阶段模糊优化方法建立一类带有补偿的模糊产销计划期望值模型,并设计含有逼近方法和粒子群优化算法的混合算法对提出的模型进行求解。给出一个实例表明模型和算法的有效性。通过改变粒子群优化算法的粒子数和迭代次数对最优解和目标函数值进行算法分析。     

马氏模型PSO及其随机过程分析

受遗传算法马氏模型理论分析的启发,提出了一种便于用马氏过程理论分析的微粒群算法。该算法中的个体仅记忆群体在进化过程中有限步内的信息,忘掉以前的信息,以建立算法的马氏过程数学模型。通过函数优化的数值模拟验证了新算法具备优良的寻优能力,同时论证了新算法是齐次马氏过程。     

Fuzzy linear programming approach to multiattribute decision making with multiple types of attribute values and incomplete weight information

In the classical Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP), the decision maker (DM) gives the pair-wise comparisons of alternatives with crisp truth degree 0 or 1. However, in the real world, DM is not sure enough in all comparisons and can express his/her opinion with some fuzzy truth degree. Thus, DM's preferences are given through pair-wise comparisons of alternatives with fuzzy truth degrees, which may be represented as trapezoidal fuzzy numbers (TrFNs). Considered such fuzzy truth degrees, the aim of this paper is to develop a new fuzzy linear programming technique for solving multiattribute decision making (MADM) problems with multiple types of attribute values and incomplete weight information. In this method, TrFNs, real numbers, and intervals are used to represent the multiple types of decision information. The fuzzy consistency and inconsistency indices are defined as TrFNs due to the alternatives’ comparisons with fuzzy truth degrees. Hereby a new fuzzy linear programming model is constructed and solved by the possibility linear programming method with TrFNs developed in this paper. The fuzzy ideal solution (IS) and the attribute weights are then obtained. The distances of alternatives from the fuzzy IS can be calculated to determine their ranking order. The implementation process of the method proposed in this paper is illustrated with a strategy partner selection example. The comparison analyzes show that the method proposed in this paper generalizes the classical LINMAP, fuzzy LINMAP and possibility LINMAP.     

考虑区间约束的物流网络双层规划模型及算法

考虑物流网络需求的不确定性,利用区间参数度量不确定性变量与参数,建立区间需求模式下的物流网络双层规划模型,设计了一种含区间参数与变量的递阶优化遗传算法,通过定义问题求解的风险系数与最大决策偏差,给出适合物流网络结构的区间运算准则,实现模型的确定性转化。以区间松弛变量与0-1决策变量定义初始种群,通过两阶遗传操作运算,求解不同情景下双层规划目标的区间最优解与节点决策方案。算例测试表明算法求解的可操作性更强,求解结果具有区间最优解与情景决策的优越性。     

车辆路径问题的轻鲁棒优化模型与算法

针对不确定旅行时间下的车辆路径问题,以总变动成本最小为优化目标,建立了一种轻鲁棒优化模型,提出了一种针对问题特征的超启发式粒子群算法.在算法中,利用基于图论中深度优先搜索的初始化策略加快算法的早期收敛速度,引入基于均衡策略的启发式规则变换方式来提高算法的寻优能力,重新设计的粒子更新公式确保生成低层构造算法的有效性.实验...     

Pricing,manufacturing and inventory policies for raw material in a three-level supply chain

We studied a decentralised three-layer supply chain including a supplier, a producer and some retailers. All the retailers order their demands to the producer and the producer order his demands to the supplier. We assumed that the demand is price sensitive and shortage is not permitted. The goal of the paper is to optimise the total cost of the supply chain network by coordinating decision-making policy using Stackelberg–Nash equilibrium. The decision variables of our model are the supplier's price, the producer's price and the number of shipments received by the supplier and producer, respectively. To illustrate the applicability of the proposed model numerical examples are presented.     

改进微粒群算法求解模糊交货期Flow-shop调度问题

针对模糊交货期Flow-shop调度问题的特点,论文提出用微粒群这种具有快速收敛、全局性能好的迭代优化算法进行求解,并使用惩罚函数、增加数据记忆库和自适应变异机制等方法对微粒群算法进行改进,减少了算法陷入局部极值的可能性。通过仿真实例,改进微粒群算法的全局寻优、收敛性和克服早熟的能力均优于遗传、启发式算法。     

多模式多资源均衡及基于动态种群的多目标微粒群算法

研究了多模式多资源均衡问题,该问题需要动态选取每项任务的执行模式,并综合考虑项目截止日期和资源限额等约束.将种群竞争模型嵌入到基于 Pareto 的向量评价微粒群算法(VEPSO-BP)中,提出了一种新的基于动态种群的多目标微粒群算法(MOPSO-DP).通过实例测试了 MOPSO-DP 的性能,并与 VEPSO-BP 进行了对比.实验结果表明, MOPSO-DP 能取得更为丰富且优化效果更好的 Pareto 非支配解.     

基于DE和PSO的混合智能算法及其在模糊EOQ模型中的应用*

设计了融合差分进化和PSO算法优点的混合智能优化算法DEPSO,通过在粒子迭代过程中,随机选择一定数量的粒子进行差分进化操作,增加粒子的多样性,使陷入局部极小的粒子逃出,以保证DEPSO的全局收敛性能,并采用典型测试函数验证了DEPSO的性能。针对模糊相关机会规划EOQ模型求解难题,设计了基于模糊模拟方法和DEPSO的智能求解算法来计算模糊事件的可信性,从而得到了使库存费用不超过预算水平的可信度最大的最优订货量,算例证实了此求解算法的有效性。     

基于混合策略自适应学习的并行粒子群优化算法

针对当前各种粒子群优化算法解决问题时存在的局限性,提出一种基于混合策略自适应学习的粒子群优化算法(HLPSO)。该算法从收敛速度、跳出局部极值、探索、开发几个不同角度融合了4种具有不同优势的变异策略,当面对不同形态的复杂问题时通过自适应学习机制选择出合适的策略来完成全局寻优。通过对7个标准测试函数的仿真实验并与其他算法相比较,所得结果表明了所提出的算法具有较快的收敛速度、较高的精度以及很强的跳出局部极值的能力。     

动态分级中心引力约束优化算法及工程应用

结合非固定多段罚函数处理约束条件,提出一种动态分级中心引力优化算法用于求解约束优化问题。该算法利用佳点集初始化个体以保证种群的多样性。在每次迭代过程中将种群分为两个子种群,分别用于全局搜索和局部搜索,根据搜索阶段动态调整子种群个体数目。对几个标准的测试问题和工程优化问题进行数值实验,结果表明该算法能处理不同的约束优化问题。     

Multimodal function optimizations with multiple maximums and multiple minimums using an improved PSO algorithm

In this paper, a multimodal function optimization problem consisting of multiple maximums and multiple minimums is solved using an improved particle swarm optimization (PSO) algorithm. In the proposed scheme, the original population needs to be randomly divided into two main groups in the first stage. One group is to tackle the maximum optimization of the multimodal function and the other then focuses on the function minimum optimization. In the second stage, each group is split up into several subgroups in order to seek for function optimums simultaneously. There is no relation among subgroups and each subgroup can individually seek for one of function optimums. To achieve that, it is necessary to enroll the best particle information of each subgroup. It means that the proposed structure contains a number of best particles, not a single global best particle. The third stage is to modify the velocity updating formula of the algorithm where the global best particle is simply replaced by the best particle of each subgroup. Under the proposed scheme, multiple maxima and minima of the multimodal function can probably be solved separately and synchronously. Finally, many different kinds of multimodal function problems are illustrated to certify the applicability of the presented method, including one maximum and one minimum, two maximums and two minimums, multiple maximums and multiple minimums, and a complex engineering optimization problem with inequality conditions.     

混沌混合粒子群算法应用于优化酯化反应神经网络模型

利用混沌映射的随机性和遍历性,将其引入粒子群优化算法,以提高算法的全局寻优能力,同时引入优进策略,以改善其局部寻优效率,在此基础上构建了混沌混合粒子群优化算法(CHPSO)。高维复杂函数的仿真优化试验表明,CHPSO全局寻优能力强、优化效率高。针对常规算法训练神经网络容易早熟收敛和陷入局部极值点的不足,采用CHPSO训练人工神经网络,由此构建CHPSO-NN模型,并应用于乙酸己酯催化酯化反应条件的建模,与BP-NN相比,其预测能力和稳健性都有较大提高,效果良好,与传统方法相比有明显的优越性。